If you want to say that it's a place you frequent, use "the". "I was at the laundry...". If you say "I was at a laundry..." it implies it was just anywhere, not somewhere you necessarily go to often. So it depends on what you're trying to communicate. By saying in your question "specific to me" I suppose you mean the former - "the laundry shop" - a place you routinely go to. It is the same thing as when we say "I was sitting on THE sofa last night". We say this because it's clearly something specific to you. It is your sofa. The fact that the listener doesn't know the specifics about your sofa doesn't change that. "I was at a friends place, and I was sitting on the sofa...". It is still "the" because there is only one of relevance, namely "your friend's sofa". To illustrate the point, you could replace "the sofa" with "my friend's sofa" (but it's unnecessarily verbose).